Reasoning, convincing and proving

problem
Impossible sums

Age

14 to 18

Challenge level

Which numbers cannot be written as the sum of two or more consecutive numbers?
problem
Different products

Age

14 to 16

Challenge level

Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
problem
What does it all add up to?

Age

11 to 18

Challenge level

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
problem
Adding odd numbers

Age

11 to 16

Challenge level

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?
problem
Three consecutive odd numbers

Age

11 to 16

Challenge level

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?
problem
Where are the primes?

Age

11 to 16

Challenge level

What can we say about all the primes which are greater than 3?
problem
Fred's maths problems

Age

16 to 18

Challenge level

If the statement is not true, what can we say will be true?
problem
Two cubic equations

Age

16 to 18

Challenge level

Which statement correctly describes the real roots of the equation?
problem
Logical cards

Age

16 to 18

Challenge level

Which of the cards provides the counter example?
problem
Three neighbours

Age

7 to 14

Challenge level

Take three consecutive numbers and add them together. What do you notice?